Parameter estimation of linear systems from frequency response measurements.
Abstract:ESDU 90006 assumes that the system is modelled by a set of coupled second-order differential equations with constant coefficients, and that a set of frequency response data is available from forced harmonic excitation of the system over a frequency range that adequately encompasses the significant resonant modes of the system. For systems all of whose response modes are lightly damped (damping ratios less than 0.2), a method is given for estimating from a Nyquist plot of the frequency response the natural undamped frequencies and damping ratios of all modes, even those whose resonant frequencies are close together. From those system characteristics, a sufficient number of initial estimates of the unknown parameters can be evaluated to provide initial values for an interactive parameter estimation procedure. An objective function is formed from the sum of the squares of the differences between measurements and model predictions and is minimised with respect to each parameter in turn. The set of non-linear equations that results is solved iteratively by the Newton-Gauss procedure. A worked example using a two-degree-of-freedom coupled system illustrates the use of the technique.
Other ESDU documents deal with parameter identification by computer-based optimisation techniques, ESDU 87039 and ESDU 88011 in the absence of process noise and ESDU 89032 when process noise is present.
|Data Item ESDU 90006|